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ACT Prep #3
Question 1: What is sec(a)sin(a) + csc(a)cos(a) , if a = 45
^{o}
?
√2
2
1
1/√2
1/2
Question #2: In the standard (x,y) coordinate plane, 3 corners of a square are (4, –3), (–4, 3), and (–4, -3). What are the coordinates of the square’s fourth corner?
(1/4, –1/3)
(4, 3)
(3, 4)
(-3, 4)
(3, -4)
Question #3: Prizes totaling $60,000 were awarded unequally between 3 contestants. Which of the following choices could be the highest prize?
$5,000
$10,000
$15,000
$25,000
$65,000
Question 4: What is the area of rectangle ABCD if the length of the side AB is 5?
40
50
25
25√3
15√3
Question 5: What is the circumference of circle O from the figure below if the length of the sides of the ABCD square is 5 inches?
10·¶ inches
5·¶ inches
¶ inches
16 inches
12 inches
Question 6: Ellipse (x - 3)
^{2}
/9 + (y - 5)
^{2}
/5 = 1 is inscribed in circle O. The transverse of the ellipse is also a diameter of the circle O. The equation that describes circle O in the standard (x,y) plane is:
(x + 3)
^{2}
+ (y + 5)
^{2}
= 3
^{2}
(x - 3)
^{2}
+ (y - 5)
^{2}
= 1
(x - 3)
^{2}
+ (y - 5)
^{2}
= 3
^{2}
(x - 3)
^{3}
+ (y - 5)
^{3}
= 3
^{3}
(x - 3)
^{2}
+ (y - 5)
^{2}
= 7
Question 7: The marked price of the shirts in a store is $25. During one week, the store sells m shirts at the marked price and n shirts discounted 25% of the marked price. Which of the following is an expression of the average price of the shirts sold?
($25m + $18.75n) /(m + n)
($25m + $18.75n) /(2m + 2n)
$25m + $18.75n
($25 + $20) /(m + n)
(m + n) / ($25m + $20n)
Question 8: A box contains 7 blue marbles, 4 red marbles and 6 green marbles. How many additional blue marbles must be added in the box so that the probability of randomly drawing a blue marble is 1/2?
2
3
4
5
6
Question 9: A number is increased 50% and the resulting number is decreased 50%. The final number is what percent of the original number?
50%
125%
75%
100%
105%
Question 10: The inequality 2x + 3 > 5x - 6 is equivalent with which of the following inequalities?
x > 6
x < 6
x > 3
x < 3
x < 10
Review the correct answers here.